Artillery computer



June 1955 R. B. BLACKMAN ETAL 2,710,720

ARTILLERY COMPUTER Filed Oct. 28, 1943 1Q Sheets-Sheet 5 FIG.

[NVE

i I Mr W W HWBODE- m v M A 7' TORNE Y June 1955 R. B. BLACKMAN ETAL 2,710,720

ARTILLERY COMPUTER Filed Oct. 28, 1943 10 Sheets-Sheet 6 cos PHASE SHIFT NETWORK SUHHING AMPLIFIER FIG/6 SUNUING AMPLIFIER F/ 15 W 7 /vvmropsRg-fi gggg i By wwmu AT TORNE 1 June 14, 1955 R. B. BLACKMAN EI'AL 2,710,720

ARTILLERY COMPUTER Filed Oct. 28, 1943 10 Sheets-Sheet 7 387 380 38/ v Q 2871 0,, aas r g aaa 385 gases 352 l p RBBLAC/(MA/V A TTORNEY June 1955 R. B. BLACKMAN ETAL 2,710,720

ARTILLERY COMPUTER Filed Oct. 28, 1943 10 Sheets-Sheet 9 R. B BLACKMAN r i V JNVENZOPS H W800ihim ATTORNEY June 14, 1955 v R. B. BLACKMAN ETAL 2,710,720

' ARTILLERY COMPUTER A TTUPNEV United States Patent ARTILLERY COMPUTER Ralph B. Blackman, Cranford, N. J., and Hendrik W. Bode, New York, N. Y., assignors to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application October 28, 1943, Serial No. 508,052

32 Claims. (Cl. 23561.5)

This invention relates to antiaircraft artillery computers and particularly to computers in which some of the data are represented by electrical quantities.

The object of the invention is a methodand means for' directing artillery fire to the future p sition of a moving target.

A feature of the invention is a computing system in which the increments in the data from a predetermined past instant to the present instant are registered and used to predict the increments in the data from the present instant to some future time.

Another feature of the invention is a one plus method of computation, that is, the values of the data at the present instant are continuously registered and the increments in these data are computed, the data for the future position being made up of the registered data plus the computed increments.

Another feature of the invention is a method and means of computation by finite differences in which the absolute changes in the observed data during one timed interval are used to predict the absolute changes in the data during the predicted time interval from the present to the future position of the target.

Another feature of the invention is a method and means of computing the position of the target in rectangular coordinates having a moving origin at the present position of the target and an orientation related to the direction of the line of sight.

Another feature of the invention is a plurality of voltage sources respectively varying with functions related to the predicted position of the target from which desired fractions of these voltages may be obtained which when added together will produce voltages proportional to the ballistic corrections required in the computations.

A further feature of the invention is a method and means of computing the dead time correction directly from the coordinates of the present and the predicted positions of the target and not, as heretofore, from the rate of change in the computed value of the time of flight.

The movement of the target from some past instant t1, when the target was at the position P1, to the present -time t2, when the target is at the position P2, is continuously measured. The elapsed time interval from the past instant t1 to the present instant t2, and the increments in the measured data during this elapsed time interval, are registered. Thus, as, in effect, the computer remembers what the movement of the target has been 2,710,720 Ce Patented June 14, 1955 corrected for dead time, and produces voltages proportional to the predicted coordinates of the target at the predicted point P5. The computer also selects a virtual target Pv for the gun and produces voltages proportional to the coordinates of this virtual target corrected for ballistic effects and the parallax from the point of observation to the gun, to give a point of burst Pb. The computer compares the voltages relating to P3 with the voltages relating to Pb, and, if there is a difference, adjusts the selected time of flight and the selected virtual target, properly corrected, until the difference is reduced to zero and Pa coincides with Pb. The values of the coordinates of the future position P: are then correct and may be transformed into firing data and transmitted to the guns. When observing a moving target the computer is continuously selecting and comparing these values and continuously sending firing data to the guns.

' In the drawings:

since thetirii' nTtlTeinstafit ti may conveniently be vations, the computer selects a time of flight, properly Fig. l diagrammatically shows in plan the geometrical relations;

Fig. 2 diagrammatically shows in elevation the geometrical relations;

Fig. 3 diagrammatically shows the time distance relalations of the flight of the projectile;

Fig. 4 diagrammatically shows the mechanism involved in the computation of range;

Fig. 5 diagrammatically shows the mechanism involved in the computation of azimuth angle;

Fig. 6 diagrammatically shows the mechanism involved in the computation of elevation angle;

Figs. 7 and 8 show a plurality of potentiometer windings and wipers;

Fig. 9 shows certain functions of slant range;

Fig. 10 shows certain functions of elevation angle;

Fig. ll schematically shows circuits for computing ballistic corrections;

Fig. 12 schematically shows circuits for computing Dre and Era and dead time correction;

Fig. 13 schematically shows circuits for computing D32, A12, E32;

Fig. 14 schematically shows circuits indicating when the target has diverged from the predicted course;

Fig. 15 schematically shows a summing amplifier used in Figs. 12, 13, 14;

Fig. 16 schematically shows the servo-motor control used in Figs. 12 and 13; and

Fig. 17 schematically and diagrammatically shows the supervisory system.

The following symbols will be used in discussing the basis of the computations:

D=slant distance E=angular height A=angle of azimuth x, y, z rectangular coordinates (north, east, up) at observing point These symbols will be used with single subscripts.

1. To designate values with respect to the observation station corresponding with the point P1 occupied by the target t seconds in the past (past position or 2. To designate values with respect to the observation station corresponding with the point P2 occupied by the target at the present time,

3. To designate values with respect to the gun corresponding with the point P; which will be occupied by the target at a time TF seconds in the future (future position). TF=t3-t2,

TF=time of flight of the projectile,

ta=dead time,

22am setting in seconds (equals TF when 14:0).

Literal subscripts: W for wind, 1 for parallax, F for firing values.

Double subscripts denote diflercnces, D21 D2-Dt,

AtvG=Aiv-AG, AW3- -AW-ri3.

Quadrant elevation is a special name for Er.

Superelevation is a special name for EF3='EFE3.

Fig. 1 shows the projection on a horizontal plane of the course of the target P1, P2, P3 the observing instrument or tracker T, the battery B and the point C which is the point in space to which. neglecting superaltitude the gun must be pointed and the fuze set so that allowing for an increase 11 in horizontal range and a deflection d due to wind. drift and other ballistic effects, the shell will burst at P3. the future position of the target. The points P1, P2, P3 respectively correspond with the positions of the target at the past time or memory point," the present time, and the predicted future time. Assuming that the target moves at uniform speed in a straight line, the line segments P1P2. and P2P3. will be in the ratio of t, the elapsed time. to TF, the predicted time, or time of flight of the shell.

The target is brought under observation at some past time and is kept continuously under observation. By means of known optical. sonic or radio instruments, the azimuth angle A of the target with respect to some arbitrary axis. say the north-south direction. is continuously measured. say in a clockwise direction. together with the angular height E, above the horizontal and the slant distance D.

At a selected past time when the target is at the past position or "memory point" P1. the angular height E1 is registered and the measurements of the increments in the angular height Eat. the azimuth angle A21, and the distance D21 commence.

At the moving present time. 1 seconds after the selected past time, the target is at the moving present position P2, having the coordinates A2, E2. D2.

In the present system a time of flight TF of the shell is selected and from the measured increments in the data during the known elapsed time. t. and the time of flight, TF, the coordinates of the future position of the target may be computed. Also the azimuth angle and the quadrant elevation of the gun and the fuze number which should cause a hit at the future position are assumed in the same coordinates. The two values of coordinates are compared and if there is a disagreement the proper elements in the data are automatically changed to reduce the disagreement to zero. The corrected values of azimuth angle. quadrant elevation and fuze number are used in firing the shell.

The distances measured from the memory point to the present position are to the predicted distances as the elapsed time t is to the time of flight TF. Thus. if a voltage be generated having an amplitude proportional to a measured distance and this amplitude is modified in the ratio IE I the modified voltage will be proportional to the predicted distance.

INCREMENT lN AZIMUTH ANGLE A32 The predicted increment in azimuth angle is computed by means of the linear increments in a horizontal axis perpendicular to the direction to the present position of the target and having the origin at the present position.

Fig. 1 shows the projections on a horizontal plane of the gun or battery B, the observing device or trackerT and the course of the target P1, P2, P3.

The gun parallax or distance from B to T is measured in rectangular coordinates X Yp having the origin at B and convenient directions, such as north, south and east,

west.

If D1 is the slant distance and E1 the angular height of the target at the memory point, the horizontal projection of this distance will be D1 cos E1. Similarly, the horizontal projection of the slant distance to the present positiOn is D: cos E2, and the horizontal projection of the slant distance from the battery B to the virtual point of aim C is D3 cos E3.

In Fig. 1, lines h-e, f-g, i-P3, Pt-n, art-ac, are drawn perpendicular to TPz; lines c-T, Bf, Ig, m!(ld, Pz-a, are drawn parallel to Tlz. BN and TN are in the direction of zero azimuth angle, thus angle NTP1=A1; angle NTP2=A:; angle NBC=A3. Using the convention A21:A2Al. angle P1TP2=A21; angle fBCz/tza. Also, as bT is perpendicular to TN, angle bTc=%-A,

and angle (Ml-1A1. As B] is parallel to Tl: anglc NBe=A2. The deflection d is perpendicular to the line of fire, thus angle and, as angle fligxangle Bgl, angle and angle iPag /la'z.

The projection of TPi on a perpendicular to TP: will equal Pl-fl, which is D1 cos E1 sin A21, and is a measured value.

The projection b-c of Yp is Y cos A2. the projection be of Xp is Xp sin A2, thus the projection c-e is Xp sin A2Y cos A2.

The projection fg is (D: cos Ez-l-h) sin A32.

The projection Pai is d cos A32.

The total predicted projection from P2 to P3 is X,, sin /l2-Yp cos A:+(DJ cos E1+h) sin Asz-l-tl cos A32.

Let

53:03 COS Ea+lt Then In Fig. 2, the points P1. P1. P3, are the projections of the past, present and predicted positions of the target, B and T are the projections of the battery and tracker, on the vertical plane containing the tracker and the present position of the target.

Point C with respect to B. and point Pl with rcspect to T are not projections. but show the true relatIonship with respect to slant distance and angular height of the point C with respect to the battery B. and of the memory point Pl with respect to the tracker T. In other words. the vertical plane containing Pi and T is rotated about a vertical line through T till this plane coincides with the plane containing P2 and T. The vertical plane containing B and C is rotated about a vertical line through B until it is parallel to the plane containing P2 and T, then translated into coincidence with the plane containing P2 and T. Lines CPz, P1'P1. Ty, and 8''; are horizontal; thus angle PiT/ Ei; angle P2T '=Ez: angle PiTlz-xlz'ni; angle CBk=Ez. Lines Cp. B't', tT, Pi'm are parallel to TPz, thus angle pC13'=E2, CB'rz/z'gz. mli'li -[lr Lines rT and Pan arc prolongations of Tlz. Lines .rr. wT, Cq, Pl, uPi, nl are perpendicular to Tlz. and lines Tr, Ck, Ptu, P1] are vertical. Thus angle In Figs. 1 and 2, the horizontal distance T-a is evidently D1 cos Er cos A21. In Fig. 2,'the distance T is Asa-d sin Asa-D3 cos E3. Applying the relationship cos A 1-2 sin C-Ps' equals S -8 .2 sin -d sin A3g-Dg 9ps E;

and from Equation 1, S3Ds cos E3=h, thus the line segment C-Pa equals h-SmZ sin sin A52 INCREMENT IN ANGULAR HEIGHT E32 The increment in angular height E32 may be computed by projecting the line segments ET: and P2P:' on an axis perpendicular to P21 passing through P2.

The horizontal line segment P1'P1 as before is D; cos E1.2 sin thus the line segment Pim is D cos E .2 sin The line segment Pin is D1 sin E21, thus the line segment mn is sin E,

D1 sin Em-D COS E -2 Sill 2 and this is the projection of a measured distance.

The projection Pa'p is the horizontal line segment CPs multiplied by sin E2 and thus equals (ii-s32 sin -d sin A3,) sin E,

sin E,

The projection Cq equals D3 sin E32.

From Fig. 1, the horizontal distance from B to T is Be plus cT or Xp cos 112+ Yp sin A2, and this equals Br in Fig. 2. Thus rs equals (Xp cos A2+Yp sin A2) sin E2.

The projection rt equals Zp cos E2.

Thus the projection of the line segment Pa'Pz is 1)3 sin E32+(s3.2 sin -h+d Sin A sin 151 (X, cos A i-Y sin A sin E -Z, cos E2 and this is the projection of the predicted distance.

The measured distances are to the predicted distances as t to TF, thus the measured distances multiplied by may be equated to the predicted distances, hence D3 sin E3g+ S3.2 Sill sin A31) Sill i (X, cos A i-Y, sin A,) sin E i-Z, cos E 3 INCREMENT IN SLANT RANGE The increment in slant range D32 may be computed with allowance for the gun parallax by projecting the In Fig. 2 the distance Tn equals D1 cos E21; the distance P m, or nu equals (D cos E 2 sin cos E the distance TPz is D2 thus, the projection P u equals D cos E D cos E 2 sin cos E ;-D;- or

-(D,D cos E +D cos E 2 sin cos E and this is a measured value.

In Fig. 2, the distance TF2 equals D2; the distance Bq equals D3 cos Eaz; the distance qv equals (Iv-8 .2 sin -11 sin A cos E the distance B's equals (Xp cos A2+Yp sin A2) cos E2; the distanceTt or sw equals Zp sin E2, thus the projection P 0 equals D D cos E3g- (ii-s52 sin %-a sin A cos E ll (X, cos A i-Y, sin A cos E l-Z, sin E,

- 2+ a COS E32) (8,2 sin h+d sin A cos E (X, cos A i-Y, sin A cos E f-Z, sin E and this is a predicted value.

Thus, #(m-m cos E +D cos E .2 sin cos E D3 COS Egg-(83.2 Sill Sill A32) COS (X, cos A- +Y,, sin A cos Eg-Z sin Eg-Dz Let S (D cos E 2 sin +8 2 sin h+d sin A -l-X cos A i-Y, sin A; Substituting the identities cos E =l2 sin and cos E =12 sin and rearranging from Equations 2, 3 and 4 are obtained the following equations for the increments in azimuth angle, angular height and slant range.

S sin Agg'i'd cos A +X, sin A Y,, cos A (D1 005 E sin A21) =0 The measured values of slant range are continuously supplied by the usual transmitters on the observation instrument to the receivers 1, 2, Fig. 4, which may conveniently be in the form of coarse and fine self-synchronous receivers. The movements of receivers 1, 2 may be indicated on suitable dials 3, 4. The shaft 5 of the line segments Pi'Pz and P2P;\' to the slant distance TPz. coarse receiver 1 is connected to the shaft 6 of the fine the slant range D: to the present position of the target.

At some desired time in the past, that is, at the memory point the clutch was operated. The clutch 15 may conveniently be a magnetic clutch controlled by a push-button or switch located at some convenient point, as shown in Fig. 17. After the clutch 15 is operated, the shaft 12 can move the potentiometer wiper 16 to select a voltage proportional to D21, the increment in slant range from the selected past time or memory point to the present time.

The shaft 12 drives one gear of the differential gear 17.

The servo-motor 18 is controlled by the computing circuit, as explained later, to drive the shaft 19 moving the wiper 20 proportionately to the increment in slant range Dan from the present position to the future position, and driving one gear of the differential gear 17.

The differential gear 17 adds the rotations of the shafts 12 and 19 to produce a rotation of the shaft 21, and a movement of the wiper 22 proportional to the range D: to the point of aim.

The shaft 21 drives the shaft 23 rotating one gear of the differential gear 24.

The servo-motor 25 is controlled by the computing circuit, as explained later, to drive the shaft 26, moving the wiper 27 proportionately to the correction for fuze number Dru, and driving one gear of the differential gear 24.

The differential gear 24 adds the rotations of the shafts 23 and 26 to produce a rotation of the shaft 28 proportional to the fuze number range Dr, which is in the form of the fuze number Z. The shaft 28 produces an indication of the number on the dial 29, and drives the selfsynchronous transmitter 30 to send the fuse number to the fuse setter.

The measured values of the azimuth angle A are transmitted from the observing instrument by the usual coarse and fine self-synchronous transmitters to the coarse 31 and fine 32 self-synchronous receivers, Fig. 5, which indicate the angle on the dials 33, 34 and, assisted by the torque amplifier 35, rotate the shaft 36 proportionately to the angle A2.

The shaft 36 drives the shaft 37 moving the Wipers 38 and 39 in proportion to the present value A: of the azimuth angle.

The clutch 40 which may be a magnetic clutch as shown in Fig. 17, is operated by a push-button or switch at the predetermined past time and moves the wiper 41 in proportion to the increment A21 in the angle.

The shaft 37 drives one gear of the differential gear 42.

The servo-motor 43 is controlled by the computing circuit. as explained later, moving the wipers 44, 45 proportionately to the computed increment A32 in the angle, and driving one gear of the differential gear 42.

The differential gear 42 adds the rotations of the shaft 37 and servo-motor 43 to produce a rotation of the shaft 46 proportional to A3. 7

The direction to which the wind is blowing has an azi muth Aw, which is put in by the handwheel 47, which rotates the dial 48, and one gear of the differential gear 49. Another gear of the differential gear 49 is driven by the shaft 46. The differential gear 49 subtracts the rotations of the handwheel 47 and the shaft 46, moving the wiper 50in proportion to the difference Aw Aw-A in the azimuth angles.

The difference angle Ara:ArAa would normally be added to the future position angle A3 to give the angle of train Ar. This addition would require another differential gear and, as the correction is small compared to the angle, may be avoided by using the voltage selected by the wiper 50 to assist in the control of the servo-motor 43, in such manner that the shaft 46 is moved in proportion to AP. The rotation of the shaft 46 is transmitted by the coarse 51, and fine 52, self-synchronous transmitters to the battery.

The measured values of the angular height E are transmitted from the observing station by the usual coarse and fine self-synchronous transmitters to the coarse 61 and fine 62 self-synchronous receivers, Fig. 6, which indicate the angle on the dials 63, 64 and, assisted by the torque amplifier 65, rotate the shaft 66 proportionately to the angle E2.

The shaft 66 moves the wipers 6 68 in proportion to the angular height E: to the present position of the target.

At the predetermined past time or memory point the clutch 69 which may be a magnetic clutch as shown in Fig. 17, is operated, say by a push-button or switch, moving the wiper 71 in proportion to the increment E21 in the angular height. At the same instant the clutch and brake 70, shown in greater detail in Fig. l7, is operated. stopping the wiper 72 at a point where the wiper 72 selects a voltage proportional to the cosine of the angular height IE1 at the past or memory point.

The servo-motor 73 is controlled by the computing circuit, as explained later, to move the shaft 74 and wiper 75 proportionally to the predicted increment E32 in the angular height from the present to the future position of the target.

The shaft 66 rotates one gear, the shaft 74 another gear of the differential gear 76. The differential gear 76 adds these rotations, moving the shaft 77 and wiper 78 proportionally to the angular height E3 to the future position of the target.

The servo-motor 79 is controlled by the computing circuit, as described later, to rotate the shaft 80 and wiper 81 through the superelevation angle EF3 to the corrected future position.

The shaft 77 drives one gear, the shaft 80 another gear of the differential gear 82. The differential gear 82 adds these rotations rotating the shaft 83 proportionally to the quadrant elevation Er. The rotation of the shaft 83 is indicated on the dials 84, 85 and is transmitted by the fine 86 and coarse 87 self-synchronous transmitters to the battery.

The wipers in Figs. 4. 5 and 6 are shown associated with potentiometer windings concentric with the driving shafts and, as indicated, more than one potentiometer winding may be arranged concentrically with a given shaft.

The potentiometer windings or cards may conveniently be made from a thin sheet of insulating material closcly and uniformly wound with insulated resistance wire. One edge of the card should be substantially straight, and the resistance wire bared to provide a good rubbing contact with the wiper. The other edge of the card is cut to produce a variation in width which will produce the Thus, for a sinusoidal variation of the selected voltage for the larger potcntiometers, the discs may have eleven clearance holes and one threaded hole.

Tm d Tm A couple of W) T F A insulated pins are usually forced into two of the clearance holes to center the assembly. Thus, the smaller Smnlarly for a cosmusoldal Vananon of voltage 5 disc has a capacity of six brushes, and the larger assemw fi. A bly a capacity of ten brushes. The brushes may be of unequal lengths and respectively associated with cards To Obtain flvohfige Variation of the form 1/2 retained in different annular spaces, or two or more of the potentiometer Winding will y in resistance P the brushes may be of the same length and associated unit length With Sin Similarly, With the identity with two or more cards retained end to end in the same 2 A annular space. The zero points of the cards are apsm E propriately offset to agree with the zero positions of the the potentiometer winding will vary in resistance per assotftatefl brushe,s' f type of potentiometer unit length of Card with sin Thus the windings for bly is disclosed in United States Patent 2,403,989, 18- these functions will have the same variation of resistt5 sued July 1946, to Manmaance per unit length of card as for cos A. For cos A In cases where the voltage selected is proportional Zero degrees has unit positive voltage, ninety degrees has to an angle: Such as the angular f Whtch cannot zero voltage, one eighty degrees has unit negative voltexceed two fight angles, two Potenttometet' cards age and two seventy degrees has zero voltage. For A I be placfid to end same P land two WIPers (1 cOSA) or 20 respectively in contact with the windings and mounted A at any desired angle apart, may be brought out to sepa- E1 5 rate slip rings.

Also, if a winding has a resistance varying per unit 2er9.degree1S has Zero Y ninety i has zl length with a cosinusoidal function so that the voltage a one 61g f h 1 t f: selected by a wiper varies with a positive sinusoidal funcvo age an two Seventy egrees as 5 p051 we v0 tion, the voltage selected by a wiper displaced 180 defunctions may be obtauieq from f' grees from the first wiper will vary with a negative nometer wnidllngs g g i vaniltlon F fi sinusoidal function, the voltage selected by a wiper hava.nce per mm engt y c angmg t e poms o app Icaing an angular lead of 90 degrees will vary as a positive of voltage The cosinusoidal function and the voltage selected by a wiper i having an angular lag of 90 degrees will vary with a 4 negative cosinusoidal function. is more accurate for Small angles than V2 0- The ballistic data relating to a gun and its ammuni- The potentiometer Cards may convementty tion are usually tabulated in terms of the slant range ed as Shown in A f 'y base 90 )Vhlch m and angular height of the future position of the target. form a hearing for the Shaft 91 15 formed wlth Senes The various corrections are tabulated for a series of of concentric ribs or buttresses 92, 93, 94, 95 separated values f Slant range f each f a Series of values f by annular spaces. If the base 90 be made of conducthe angular height ttvfi material, strtps of insulating material 96 may be A mathematical analysis of the tabulated ballistic data Placed on each The potehtlPmetet cards are shows that the various corrections may be expressed as Wrapped y the mattmal Another SttlP functions of the slant range D and angular height E to of matel'lat Whlch may be msulatmg mammal P the future position of the target. These functions are be pp tlghtly around Over the card drawn ttght linear combinations of twelve functions, four functions and the ends fastened together or small wedges may be of slam range, f functions f Slam range times a between the a the catdends of 4.3 quantity resembling a sinusoidal variation and four functhe Wmdtngs may be led out to Suttable tetmtnals tions of slant range times a quantity resembling a cosinusported by the base 90. oidal variation The WlPerS In"ty be mounted an m5u1atmg time 98 Thus all of the ballistic corrections may be matched concentric with the shaft 91. Ii111;1 rfings1 9g, 100,l101, by afiunction of the general form 102 are mounted concentric wit s a t ut insu ated therefrom, alternating with insulating discs 98, 103, 104, do (I0) 105. The respective brushes are secured by screws, K such as screw 106, passing through clearance holes in +Ah(D)+Bh'(D)s(E)+CMDFKE) the intervening slip rings, and threaded into the corre- The constants in Equation 10 for the corrections of sponding slip ring. The complete assembly of wipers, the time of flight and elevation angle for non-standard slip rings and insulators may be keyed to the shaft 91. muzzle velocity; the corrections of the time of flight and The brushes, such as 107, connect the wipers to any elevation angle for non-standard air density; the correcdesired circuit. tions for cross wind and drift; and the time of flight, For the smaller potentiometers, the slip ring discs may superelevation and fuze correction for a particular gun have seven clearance holes and one threaded hole, while, are given in Table 1.

Table 1 Muzzle Velocity Air Density Cross Time oi Eleva- Time oi Elevawind Drm TF SE F0 Flight tion Flight tion In addition the fuze calibration correction FC has further corrections of -.061 times the time of flight correction of muzzle velocity and .022 times the time of flight correction of air density.

The time of flight correction of muzzle velocity is expressed as the correction in the time of flight for 100 feet per second change in muzzle velocity.

The elevation correction of muzzle velocity is expressed as the correction in superelevation in mils (1600 mils equals 90 degrees), for 100 feet per second change in muzzle velocity.

The air density corrections are similarly expressed as corrections in time of flight and superelevation for per cent change in air density.

The cross wind correction is in yards for a mile per hour wind.

The drift is in yards, negative to the right of the line of fire, but the offset A0 is in mils (1600 mils equals degrees), clockwise.

The time of flight is in seconds, the superelevation in mils, and the fuze calibration is time ofvflight in seconds less fuze number.

The A0 coetlicients, which occur only in connection with the superelevation. fuze calibration correction and drift, are obtained by mechanically offsetting the output dials.

The 1:1(D), 112(D). 11:;(D), and 114(D) voltage functions are plotted in Fig. 9 against the range. The functions shown are the voltage functions, not the potentiometer cards. as discussed hereinabove, will vary approximately with the derivative of the function. This relationship is rigorously true only if the potentiometer is purely a potential divider, that is, when no current is drawn from the wiper. In the present case, the wipers 22, 118, 119, 120 of the range potentiometers supply current to the other potentiometers and the resistance network thus, the widths of the potentiometer cards do not vary exactly with the derivative of the voltage function, but are modified to correct for the effects of the currents drawn from the wipers.

The .II(E), c1(E). s2(E), czlE). ss(E), @(E), 54(13), citE) voltage functions are plotted in Fig. 10 against E the angular height. The angular height has been expressed in mils. where 1600 mils equals 90 degrees. The angular height will not exceed 1600 mils of elevation, and some 200 mils of depression, a total angle of about 1800 mils. If two potentiometer cards, each extending over this angle, are placed end to end as arcs of the same circle. they will occupy only 202 /2 degrees of the circumiercnce of the circle. To secure a better scale factor, the cards may be spread out, say in the ratio of 5 to 3, to cover 337 degrees. with a corresponding increase in the angular travel of the wiper. In Fig. ID

the voltage curves have been plotted against the angular height in mils and a scale of the actual circumferential angle has been added.

Like the functions lz(D), the functions shown in Fig. l0 are voltage functions, not potentiometer card shapes. The widths of the potentiometer cards will be the derivative of the functions shown. modified to take into account the currents drawn by the resistance network from the various potentiometer wipers.

The S1 and (-1- functions together are a true sinusoidal Junction extending over: 3200 mils and, as theJznfune tion is linearly related to the range. the ct voltage will be proportional to its cos E3, the horizontal range of the target in the future position.

The Si function is a sinusoidal function, not of E but of (E: 367.1). The positions of the wipers 124, 125 for zero angle is indicated by the small arrowheads and the complete travel of the wipers in mils is also indicated. The travel of the st wiper overlaps the travel of the crwiper. The voltage at the mid-point of the winding is of unity magnitude. The voltage at zero The width of the potentiometer cards,

angle and at the end of the travel of the ct wiper is zero, that is, ground potential.

The s: function varies from unity voltage for the first 200 mils to zero voltage, or ground, at 1600 mils.

The 02 function varies from zero at -200 mils to unit voltage at about 1073 mils, and .7863 voltage at 1600 mils. The positions of the wipers 128, 129, for zero angle, are indicated by the small arrowhead.

The s; and 03 functions overlap, the c3 wiper 133 being spaced only 400 mils from the sa wiper 132. The complete function varies from unit voltage at 200 mils to about 15 percent of unit voltage at 1500 mils, rising to 61 per cent of unit voltage at 2000 mils.

The 54 function varies from zero voltage at zero angle to unit voltage at about 1000 mils and zero voltage at 1600 mils. The as function rises from zero at zero angle to unit voltage at 1600 mils. The positions of the wipers 136, 137 for zero angle, are indicated by the small arrowheads.

In Fig. 11 current from a suitable source 110, such as an oscillator, is supplied by the tapped transformer 111 to the potentiometer windings 112, 113 and to the primary windings of the transformers 114, 115. In order to equalize the loads on the two sections of the secondary winding of transformer 111, the windings 112, 113 are connected across one section, while the transformers 114, 115 are connected across the other section. The secondary windings of transformers 114, 115 are respectively connected across the potentiometer windings 116, 117.

The windings 112, 113, 116, 117 are indicated on Fig. 4 in association with the wiper 22. The wipers 118. 119, 120 may be associated with the wiper 22, similarly to the four wipers shown in Fig. 8. The zero points of the respective windings 112, 113, 116, 117 will, of a course, be offset to correspond with the zero positions of the wipers 22, 118, 119, 120. The wipers 118, I19, 120 are moved, like the wiper 22, by the shaft 21, Fig. 4, proportionally to the slant range D3.

The winding 112 is of uniform resistance, so that the voltage selected by the wiper 22 is proportional to hitD), Fig. 9, that is, to D3.

The voltage selected by the wiper 22 is supplied to the primary winding of transformer 121.

The secondary winding of transformer 121 is in two sections, and one section is connected across the potentiometer winding 122, which has a sinusoidal variationof resistance to produce the voltage variations 51(5) and c1(E) of Fig. 10.

The voltage selected by wiper 22 is proportional to 111(D); the voltage selected by wiper 124 is proportional to /z1(D)s1(E); and the voltage selected by the wiper 125 is proportional to lt1(D)c1(E), the second. third and fourth terms of the first line of Equation 10. The term h1(D)ci(E,) is proportional to the horizontal range to the point of aim.

The potentiometer winding 113 has a resistance variation producing a voltage varying with the function /12(D). Fig. 9. The voltage selected by the wiper 118 is applied to the primary winding of transformer 126. The secondary winding of transformer 126 is in two sections, and one section is connected across the potentiometer winding 127. The winding 127 has a variation in resistance such as to produce a voltage varying with s2(E). Fig. 10. The

fiJuoltageselectedby the wiper-1281s thus proportional to.

lt2(D)s2(E).

The winding has a resistance variation such as to produce a voltage varying with the function cztE). Fig. 10. The second section of the secondary winding of transformer 126 is connected to a tap in the winding 130 and to the two ends of this winding. The voltage selected by the wiper 129 is thus proportional to hz(D)cz(E).

The voltage selected by the wiper 119 is supplied to the potentiometer winding 131. This winding has a resistance variation such that the voltages selected by the 13 wipers 132, 133 vary with the functions s3(E) and c3(E), Fig. 10. The voltages selected by the wipers 132, 133 are thus proportional to h3(D).r.;(E) and h3(D)c3(E), respectively.

The potentiometer winding 135 is arranged like the winding 130, the voltage selected by the wiper 120 being applied to a tap in the winding 135, the ends of winding 135 being grounded. The voltage selected by the wiper 120 is also applied to the potentiometer winding 138. The resistances of the windings 135, 138 vary in such manner as to produce voltages varying with the functions s4(E) and 04(E), Fig. 10. The voltages selected by the wipers 136, 137 are thus proportional to h4(D)s4(E) and h4(D)c4(E). The wipers 124, 125, 128, 129, 132, 133, 135, 137, together with wiper 78, Fig. 12, are moved by shaft 77, Fig. 6, proportionally to E3.

For convenience of description, the voltages will be designated by their characteristic constants, as follows: A wiper 22, B1 wiper 124, C1 wiper 125; A2 wiper 118, B2 wiper 128, C2 wiper 129; A wiper 119, B3 wiper 132, C3 wiper 133; A4 wiper 120, B4 wiper 136, C4 wiper 137.

As the secondary winding of transformer 111 is center tapped, the voltage from oscillator 110 is available in two phases, 180 degrees apart. Thus, these phases may be selected so as to represent the positive and negative values of the quantities in Table 1.

The phase of the voltage supplied to the potentiometer windings 112, 113, may be designated as phase, and the phase of the voltage supplied to the primary windings of transformers 114, 115 as 11 phase. Transformer 114 is so poled that the voltage from the secondary winding is of 71' phase, while transformer 115 is so poled that the voltage from the secondary winding is of 0 phase.

The phases of the voltages representing the terms in Equation will then be as shown in Table 2.

In Table 1, the highest accuracy is required for the time of flight, TF, superelevation SE, and fuze calibration FC corrections. Thus, for these corrections it is preferable that the voltages, as derived from a resistance network, be of the correct phase so that transformers are not required.

The signs of the functions and the phases of the voltages representing these functions are given in Table 3.

Table 3 TF SE Sign Phase 7 The A1 term in the FC correction is derived in a special manner, as explained hereinafter.

The muzzle velocity may be more or less than the standard muzzle velocity, the air density may be greater or smaller than the standard air density and the cross wind may blow from the left-hand or the right-hand. These three corrections must be available in both phases. As the accuracy required for these three corrections is not too high, the voltages of both phases may be obtained by supplying the voltage representing the correction to the primary windings of a transformer having two primary as well as two secondary windings. The secondary windings then give the voltages of both phases. The signs and phases of the voltages representing these functions are given in Table 4.

' verse of the phases of the voltages.

In the MVTF correction, the signs of the A1, C2, A3 and C3 terms agree with the phases of the voltages, while the signs of the A2, B3 and A4 terms are the re- The A1, C2, A3 and C3 voltages may be supplied to one primary winding of a transformer poled to produce one phase relation in the secondary windings. The A3, B3 and A4 voltages may then be supplied to another primary winding of the same transformer poled to produce the other phase relation in the secondary windings.

Similarly, in the MVSE correction, the A3 voltage is supplied to one primary winding and the B2 and C3 voltages to another primary winding.

A similar process of phasing is used in connection with the air density and cross wind corrections.

The phase of the drift correction is reversed in a special transformer 323 in Fig. 12 which also combines the drift correction voltage with the cross wind correction voltage.

MUZZLE VELOCITY The normal ballistic tables are based upon an assumed standard muzzle velocity of the shell. A new gun will frequently have a muzzle velocity exceeding the standard velocity, but, with use, the erosion of the barrel causes the muzzle velocity to decrease to the standard and eventually to become less than the standard.

As a muzzle velocity differing from the standard will cause the time of flight of the shell to differ from the standard conditions, the time of flight must be corrected for a non-standard muzzle velocity.

In Fig. 11 current from wiper 133 flows through resistor 232, to resistors 234, 235, 239, 240, in series, producing a voltage proportional to C3 in the connection 149. v

Current from the wiper I29'tiows 'thro'tighresistor' 233 and resistors 235, 239, 240 in series, adding a voltage proportional to C2 to the connection 140.

Current from the wiper 119 flows through resistor 236 and resistors 239, 240 in series, adding a voltage proportional to A3 to the connection 140.

Current from the wiper 22 fiows through resistors 237,

v238 and resistor 240, adding a voltage proportional to A1 to the connection 140.

As the four voltage sources are intercoupled by the resistors 7234, 235, 239, 240, there will be a tendency for the voltages developed across these resistors to cause currents to fiow back through some of the sources. These circulating currents are undesirable, and they are made small by having the resistances of the resistors 232, 233, 236, 237, 238 large compared with the resistances of the resistors 234, 235, 239, 240.

Q1rrent from wiper 132 flows through resistor 246 and resistors 244, 241 in series, producing avoltage proportional to B2 in the connection 141.

Current from wiper 118 fiows through resistors 249, 243, and through resistors 244, 241 in series, adding a voltage proportional to A2 to the connection 141.

Current from wiper 120 flows through resistor 242, and resistor 241, adding a voltage proportional to A4 to the connection 141. j

The connections 140, 141 lead respectively to the ends of the primary winding oftransformer 300, Fig. 12, the center of this winding being grounded. The currents flowing in the primary winding will produce currents in the secondary winding of transformer 3Mearying in the required manner to correct for a nonstandard muzzle velocity.

'Resistors 301 and 302 in series are connected across the secondary winding of transformer 300 in parallel relationship with the winding of potentiometer 303. The wiper of potentiometer 303 is grounded and is set to the value of the muzzle velocity of the gun. The potential of the junction of resistors -1, 302 with respect to ground will then vary in proportion to the required correction.

The superelevation of the gun must also be corrected for a non-standard muzzie velocity.

Current flows from wiper 119 through' resistor 247 and resistor 248, applying through resistor 255, to the connection 142, a voltage proportional to A3.

Current flows from wiper 128, through resistor 252 and resistors 254, 250 in series, applying through resistor 256 to the connection 143 a voltage proportional to B2.

'Current fiows from wiper 133 through resistor 251 and resistor 250 adding a voltage to connection 143 proportional to Ca. V W

The connections 142, 143 lead to the primary winding of transformer 304, Fig. 12 which is grounded at an intermediate tap. The resistors 305, 306 in series, and the winding of potentiometer 3tl7 are connected across the secondary winding of transformer 304. The wiper-of potentiometer 307 is grounded and adjusted to the value of muzzle velocity. The junction of resistors 305, 306 will have a potential with respect to ground varying with the F desired correction. The wipers of potentiometers 303 and 307 are ganged to be adjusted simultaneously.

The resistors 255 and 256 aid in matching the impedance of the network to the'impedanec of transformer 304.

AIR DENSITY The normal range tables are based upon an assumed standard structure of the air. As the barometric pressure and temperature of the air at the time of firing mas deviatc from the assumed conditions, the structure of the air is measured at frequent intervals and weighted average values of the density of the air supplied to the computer. The effects of a non-standard density of the air are generally-similar to theetfects of a non-standard muzzle .velocity. 7

Current flows from wiper 118 through resistors 249 and 253, from wiper 137 through resistor 258 and from wiper 132 through resistor 260. the combined cur rents flowing through resistor 26l and applying a voltage to connection 144 made up of a voltage proportional to A2, a

voltage proportional to C4 and a voltage proportional to B3.

Current flows from wiper 22 through resistors 237, 265 and resistors 264, 262 applying a voltage through resistor 259 to connection 145 proportional to A1. a

Current flows from wiper 119 through resistor 263 and resistor 262 adding a voltage to connection 145 propor= tional to A3.

The connections 144, 145 lead to the ends or" the primary winding of transformer 308, Fig. 12, which is grounded at an intermediate tap. The resistors 309, 310 in series, and the winding of potentiometer 311 are connected across the secondary winding of transformer 308. The wiper of potentiometer 311 is grounded and adjusted to the'current value of the air density. The junction of resistors 309, 310 will then have a potential with respect to ground varying with the desired correction. The resistor 259 aids in matching the impedance of the network to the impedanceof transformer 308.

The superelevation must also be corrected for a nonstandard air density.

Current from wiper flows through resistor 266 and resistors 267, 269 in series, applying a voltage through resistor 276 to connection 146 proportional to C1.

Current from wiper 119 flows through resistor 268 and resistor 269 ad,ding a voltage on connection 146 propor'-' tional to A3.

The resistor 276 assists in matching the impedance of the network to the impedance of the remainder of the circuit.

Current from wiper 128 fiows'through resistor 275 and resistors 274, 272, 270 in series applying a voltage to connection 147 proportional to B2.

Current flows from wiper 136 through resistor 271 and resistors 272, 270 in series, adding a voltage to connection 147 proportional to B4.

Current from wiper 133 fiows' through resistor 273 and resistor 270 adding a voltage to connection 147 proportional'to C3.

The connections 146, 147' lead to the ends of the primary winding of transformer 312, which is grounded at an intermediate tap. The resistors 313, 314'in series, and the winding of potentiometer 315 are connected across the s condary winding of transformer 308. The

CORRECTION FQR WIND From meteorologic observations, a weighted average of the velocity and direction of the: prevailing horizontal wind is supplied to the computer. The corrections in the data supplied to the gunsfand in the quantities involved in the computation of these data may be made in the following manner.

The voltages tabulated under cross wind in Table I, when properly added, produce a voltage varying as the effect given in the ballistic tables for a horizontal cross wind having a velocity of sixty miles per hour. The arriplitude of this voltage is then reduced in the ratio of the actual velocity of the wind in miles per hour to sixty miles per hour.

If the actual velocity of the wind is W miles per hour, the voltage is reduced in the ratio The range winde etfect is functionally similar to the cross wind ettect and is approximately proportional to the cross wind effect. This portion of the range wind effect which may be taken; as 1.170 times the cross wind effect is added to the horizontal distance D: cos E: and

may be designated The residue of the range wind effect is applied as corrections to the time of fiight and superelevation. The

residual correction to the superelevation in mils is proportional to the horizontal distance effect in yards, while the residual correction to the time of flight in seconds is proportional to the horizontal distance effect in yards and to a function of the angular height.

For a head wind, the phases of the voltages representing the horizontal range correction, the time of flight correction and the superelevation correction must be such as to increase Dz, TF and EF, respectively. These phases are the same and may be obtained from a potentiometer wiper selecting voltages proportional to +cos Awz.

The voltages representing W W 66 and K have amplitudes proportional to the cross and range effects produced by winds of the actual velocity blowing crosswise and along the actual line of fire. The amplitudes of these voltages must, therefore, be reduced proportionally to the components of the actual wind velocity crosswise and along the line of fire.

The component of the actual velocity of the wind crosswise of the line of fire is evidently W sin Am, and the component along the line of fire is W cos Am.

The effect of a horizontal cross wind having a velocity of sixty miles per hour is a function of the voltages proportional to A1, A2 and C2.

Current flows from wiper 118 through resistors 227, 257 in series; and from wiper 129 through resistor 228; the combined currents flowing through resistor 229 and applying to connection 157 voltages proportional to A2 and C2.

Current flows from wiper 22 through resistors 237, 231 in series and resistor 230, applying to connection 158 a voltage proportional to A1.

The connections 157, 158 lead to the ends of the grounded primary winding of transformer 316, Fig. 12. The windings of potentiometers 317, 318 are respectively connected across the sections of the grounded secondary winding of transformer 316.

The voltages developed in the secondary windings of transformer 316 represent the deflection in yards due to a cross wind of sixty miles per hour, the wipers of potentiometers 317, 318 which are ganged together to move simultaneously, are adjusted to select equal voltages of opposite phases proportional to the velocity W of the wind. The voltages proportional to g sin A the deflection effect of the cross wind. This voltage is supplied to one winding oftran'sformer 323'and, as explained hereinafter, is combined with a voltage proportional to the drift to produce a voltage proportional to the deflection d in Equations 6, 7, 8.

Wiper 109 of potentiometer 322 selects a voltage proportional to W 56 cos A which is applied across the resistors 325, 326 in series.

The voltage developed across resistor 326 is applied to an input resistor of the summing amplifier 324. As the residual correction to the superelevation in mils (1600 mils equals degrees) is directly proportional to the horizontal cross wind effect in yards, the resistances of resistors 325, 326 and the amplification of this input voltage by amplifier 324 are designed to produce the proper scale factor of volts per mil for this input.

The total voltage across the resistors 325, 326 is applied across the potentiometer winding 321. Wiper 78 is moved proportionately to E3. The potentiometer winding 321 has a variation of resistance such that the voltage selected by the wiper 78 is unity from 200 mils to +5 69.1 mils and then decreases linearly with E3 down to about 16 /2 per cent of the applied voltage at 1600 mils.

The voltage selected by the wiper 78 is applied to an input resistor of the time of flight summing amplifier'319. The amplification of this input voltage by amplifier 319 is designed to produce the proper scale factor in volts per second.

As the voltages proportional to the range wind efiects are later supplied to summing amplifiers, which reverse the phase or sign of these voltages, the wiper 290 of potentiometer 322 is located degrees behind wiper 109 and 90 degrees behind wiper 50 to select a voltage proportional to 2% cos A The voltage selected by wiper 290 is applied by connection 397 to an input resistor of the summing amplifier 396, Fig. 13. A voltage proportional to D3 cos E3 is also supplied to an input resistor of amplifier 396. The amplification of the voltage supplied by the connection 397 is designed to produce a scale factor in volts per yard such that the voltage as added is proportional to W 'eo the range effect of the wind, which is the quantity h in Equation 1.

The voltage selected by the wiper 290 of potentiometer 322 is also applied to resistors 327, 328 in series, and the voltage developed across resistor 327 is applied by connection 403 to an input resistor of the summing amplifier 395. The resistances of the resistors 327, 328 and the amplification of this input by the amplifier 395 are designed to produce the proper scale factor in volts per yard for this input, which is the quantity i: in Equation 5.

DEFLECTION cos A The deflection component of the wind, or cross wind has an effect like the drift, thus the voltage selected by"; wiper 50 of potentiometer 322 is supplied to the upper end of the primary winding of transformer 323. The two voltages applied to the primary winding of transformer 323 combine in the right phase and produce a voltage across the secondary winding proportional to .i (6O S111 Ayn-FD) which is the quantity din Equations 5 and 6.

TIME OF FLIGHT OF SHELL For standard conditions, the time of flight TF of the shell may be represented by the sum of voltages proportional to A1, A2, B1, B3, C2, C4.

75 Current flows from wiper 118 through resistors 206,

19 207, 208 in series, applying a voltage to connection 148 proportional to A2.

Current flows from wiper 22 through resistors 201, 202, 203 in series, applying a voltage to connection 149 proportional to A1.

Current flows from wiper 137 through resistor 216 and resistors 283, 218, 219 in series, applying a voltage to connection 150 proportional to C4.

Current flows from wiper 129 through resistor 215, and from wiper 132 through resistor 220. the combined currents flowing through resistors 218, 219 in series, adding voltages to connection 150, proportional to C2 and Ba.

Current flows from wiper 124 through resistors 217, 219 in series in parallel relationship with resistor 245 adding a voltage to connection 150 proportional to B1.

The connections 148, 149, 150, lead, respectively, to individual inputs of a summing amplifier 319, Fig. 12, which may be of the type shown in Fig. 15. The sum of these voltages will be proportional to the time of flight of the shell for standard conditions. This voltage must be further corrected for non-standard conditions; thus connections 320, from the wiper 78 of potentiometer 321; 151 from the junction of resistors 309, 310; 152 from the junction of resistors 301, 302, also lead to individual inputs of the summing amplifier 319, supplying the re quired corrections for range wind, air density and muzzle velocity. The output circuit of amplifier 319 supplies equal voltages of opposite phase proportional to the time of flight of the shell.

SUPERELEVATION The quadrant elevation, or angle of elevation at firing, of the gun is greater than the geometric angular height E: by the angle of superelevation Era.

In Fig. 11, current flows from wiper 128 through resistor 221 and resistors 223, 224 in series, applying to connection 155 a voltage proportional to B2.

Current flows from wiper 136, through resistor 222 and resistor 224 adding to connection 155 a voltage proportional to B4.

Connection 155 leads to one input resistor of a summing amplifier 324, Fig. 12, which may be of the type shown in Fig. 16.

Non-standard conditions of muzzle velocity and air density are compensated by supplying voltages from the junction of resistors 305, 306 through connection 330, and from the junction of resistors 313, 314 through connection 331, respectively, to individual input resistors of the summing amplifier 324.

Current from oscillator 110, Fig. 11, flows by connecr tion 160 through the winding of potentiometer 332, Fig. 12. The voltage selected by the wiper 81 of potentiometer 332 is supplied by connection 333 to an individual input resistor of the summing amplifier 324.

Current fiows from connection 160 through a 90-degrce phase shifting network 334, of known type, to one phase winding of a two-phase motor 79, which is also shown on Fig. 6.

The summing amplifier 324 sums up, or adds, the various voltages supplied to the input circuit. If the sum of these voltages is not equal to zero, current is supplied by the amplifier 324 to the other phase winding of motor 79, starting motor 79, which drives the wiper 81 of potentiometer 332, changing the voltage supplied by wiper 81 to'amplifier 324 untilthe sum of the-input voltages is reduced to zero, and the wiper 81 has been moved through the angle Era.

FUZE NUMBER The fuze mechanism, for timing the burst of the shell after the gun has fired, is essentially a small, rugged, centrifugally operated clock. The clock mechanism is not a very accurate timepiece; thus, it is necessary to create voltages which will vary with the actual rate of this small clock. As the clock is driven by the spin of the shell,

5) OD, intersecting the course, ADI-l, of the target at D,

having range D3 and elapsed time 0J=TF.

But the shell is not fired until after the dead time 0C=tri has elapsed. The time range plot of the shell moving at uniform velocity is CH, intersecting the course at H.

Thus, the fuze setting is related to the time interval CK, which may be designated TF1.

Thus

M 0. -=TF-- we OC=td=FH CK=TF1 JK=TF1+ta-TF EF=TFi-TF From simple geometry EF DI IH iE 3 FH FG- HG 0A OA=D 0B=D AB=D -D these voltages must be corrected for a small change in the rate due to non-standard muzzle velocity and density of the air.

Current fiows from wiper 22, Fig. 11, through resistors 201, 204 in series, and resistor 205, applying a voltage proportional to A1, through connection 154 to an input resistor of a summing amplifier 335, Fig. 12, which may be of the type shown in Fig. 16.

Current from wiper 118, Fig. 11, flows through resistors 206. 214 in series and resistors 213, 212, 209 in series, applying through resistor 285 a voltage propor tional to A to the connection 153.

Current from wiper 129 flows through resistor 211 and resistors 212, 209, adding a voltage proportional to C2 to connection 153.

Current from wiper 128 flows through resistor 210 and resistor 209, adding a voltage proportional to B2 to connection 153.

Current from the junction of resistors 301, 302, Fig. 12, fiows by connection 152 through resistor 278 and resistors 280,.282.adding through resistor 286 to connection 153 a voltage which corrects for the change in rate with non-standard muzzle velocity.

Current from the junction of resistors 309, 310, Fig. 12. flows by connection 151 through resistor 281 and resistor 282 adding through resistor 286 to connection 153 a voltage which corrects for the change in rate with non-standard air density.

The resistors 285, 286 reduce interaction between the various voltages.

Connection 153 leads to an input resistor of the summing amplifier 335, Fig. 12.

Voltage proportional to TF is supplied by connection 336 to an input resistor of the summing amplifier 335,

Fig. 12.

After the firing data are received at the gun, the fuze must be set, the shell loaded in the chamber and the breech closed before the gun may be fired. The time taken for these actions, that is. the time from the final setting of the fuze to the actual firing of the gun, is known as the dead time. This time period cannot be accurately determined but may be estimated for any gun crew and will usually be less than four seconds. The fuze setting, as given by the time of flight determined by the geometry of the target, must be corrected for the dead time.

For convenience the target may first be considered as fiying in the line of sight from the present position. In Fig. 3 the ordinates are the values of the slant range and the abscissae are time measured from the present time, 0.

0A is the present slant range D2.

OB is the geometrical future slant range D3.

If the shell were fired at time zero, the time range plot of the shell moving at uniform velocity would be 

